Here \(H\)  stands for the mean curvature of \(\Sigma \) . Moreover, equality holds if and only if \(\Sigma \)  a round sphere. Applying the inverse mean curvature flow, Guan and Li [1]} showed that the convexity condition for (REF ) can be relaxed to mean convexity and star-shapedness. The star-shapedness can be further weakened to an outward minimizing condition using the weak inverse mean curvature flow of Huisken and Ilmanen [2]}. It is still an open problem whether (REF ) holds for general mean convex hypersurfaces.
